{
"metadata": {
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"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter8 - Hydraulic pumps"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 8.1 Page 354"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"from math import pi, tan\n",
"#input data\n",
"D=1.3#Diameter of the pump in m\n",
"Q=3.5/60#Discharge of water by pump in m**3/s\n",
"U2=10#Tip speed of pump in m/s\n",
"Cr2=1.6#Flow velocity of water in pump in m/s\n",
"b2=30#Outlet blade angle tangent to impeller periphery in degree\n",
"Cx1=0#Whirl velocity at inlet in m/s\n",
"U=10#Tip speed of pump in m/s\n",
"d=1000#Density of water in kg/m**3\n",
"g=9.81#Acceleration due to gravity in m/s**2\n",
"\n",
"#calculations\n",
"Wx2=Cr2/tan(b2*pi/180)#Exit relative velocity in m/s\n",
"E=(U2/g)*(U2-(Wx2))#Euler head in m or W/(N/S)\n",
"m=d*Q#Mass flow rate of water in kg/s\n",
"W=E*m*g#Power delivered in W\n",
"r=D/2#Radius of the pump in m\n",
"T=W/(U/r)#Torque delivered in Nm\n",
"\n",
"#output\n",
"print 'Torque delivered by the impeller is %3.1f Nm'%(T)\n",
"# Answer in the textbook is wrong."
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Torque delivered by the impeller is 274.1 Nm\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 8.2 Page 355"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from math import sin, tan\n",
"#input data\n",
"b2=30#Impeller blade angle to the tangent at impeller outlet in degree\n",
"d=0.02#Blade depth in m\n",
"D=0.25#Blade diameter in m\n",
"N=1450#Pump rotation speed in rpm\n",
"Q=0.028#FLow rate of the pump in m**3/s\n",
"sf=0.77#Slip factor \n",
"g=9.81#Acceleration due to gravity in m/s**2\n",
"\n",
"#calculations\n",
"A=3.1415*d*D#Flow area in m**2\n",
"Cr2=Q/A#Flow velocity in m/s\n",
"Wx2=Cr2/tan(b2*pi/180)#Exit relative velocity in m/s\n",
"U2=(3.14*D*N)/60#Tip speed of pump in m/s\n",
"Cx2=U2-Wx2#Absolute whirl component at exit in m/s\n",
"E=(U2*Cx2)/g#Euler head with no whirl at inlet in m\n",
"Cx21=sf*Cx2#Actual value of component of absolute value in tangential direction in m/s\n",
"Es=sf*E#Theoretical head with slip in m\n",
"Z=(3.145*sin(b2*pi/180))/((1-sf)*(1-((Cr2/U2)/tan(b2*pi/180))))#Number of blades required based on stodola slip factor\n",
"\n",
"#output\n",
"print '(a)Theoretical head with slip is %3.2f m\\n(b)Number of blades required is %3.f'%(Es,Z)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a)Theoretical head with slip is 23.65 m\n",
"(b)Number of blades required is 8\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 8.3 Page 356"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#input data\n",
"D2=0.4#Outer diameter of impeller in m\n",
"b2=0.05#Outlet width of impeller in m\n",
"N=800#Running speed of pump in rpm\n",
"Hm=16#Working head of pump in m\n",
"b22=40#Vane angle at outlet in degree\n",
"nm=0.75#Manometric efficiency \n",
"g=9.81#Acceleration due to gravity in m/s**2\n",
"\n",
"#calculations\n",
"U2=(3.1415*D2*N)/60#Impeller tip speed in m/s\n",
"Cx2=(g*Hm)/(U2*nm)#Absolute whirl component at exit in m/s\n",
"Wx2=U2-Cx2#Exit relative velocity in m/s\n",
"Cr2=Wx2*tan(b22*pi/180)#Flow velocity of water in pump in m/s\n",
"A=3.14*D2*b2#Area of flow in m**2\n",
"Q=A*Cr2#Discharge of the pump in m**3/s\n",
"\n",
"#output\n",
"print 'The discharge of the pump is %3.4f m**3/s'%(Q)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The discharge of the pump is 0.2247 m**3/s\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 8.4 Page 357"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from math import tan, atan, degrees\n",
"#input data\n",
"D2D1=2#The ratio of outer and inner diameter \n",
"N=1200#The running speed of pump in rpm\n",
"Hm=75#Total head producing work in m\n",
"Cr1=3#Flow velocity through impeller at inlet in m/s\n",
"Cr2=Cr1#Flow velocity through impeller at outlet in m/s\n",
"b22=30#Vanes set back angle at outlet in degree\n",
"D2=0.6#Outlet diameter of impeller in m\n",
"d=1000#Density of water in kg/m**3\n",
"b2=0.05#Width of impeller at outlet in m\n",
"g=9.81#Acceleartion due to gravity in m/s**2\n",
"\n",
"#calculations\n",
"D1=D2/D2D1#Inlet diameter of impeller in m\n",
"U1=(3.1415*D1*N)/60#Impeller tip speed at inlet in m/s\n",
"b11=degrees(atan(Cr1/U1))#Vane angle at inlet in degree\n",
"U2=(3.1415*D2*N)/60#Impeller tip speed at exit in m/s\n",
"A=3.1415*D2*b2#Area of flow in m**2\n",
"Q=A*Cr2#Discharge of the pump in m**/s\n",
"m=d*Q#Mass flow rate of water in kg/s\n",
"Wx2=Cr2/tan(b22*pi/180)#Exit relative velocity in m/s\n",
"Cx2=U2-Wx2#Absolute whirl component at exit in m/s\n",
"W=m*U2*Cx2*10**-3#Work done per second in kW\n",
"nm=Hm/((U2*Cx2)/g)#Manometric efficiency \n",
"\n",
"#output\n",
"print '(a)Vane angle at inlet is %3.3f degree\\n(b)Work done per second is %3.2f kW\\n(c)Manometric efficiency is %0.2f %%'%(b11,W,nm*100)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a)Vane angle at inlet is 9.043 degree\n",
"(b)Work done per second is 346.42 kW\n",
"(c)Manometric efficiency is 60.05 %\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 8.5 Page 358"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#input data\n",
"Q=75#Discharge from the pump in l/s\n",
"D1=0.1#Inlet diameter of the pump in m\n",
"D2=0.29#Outlet diameter of the pump in m \n",
"Hm=30#Total head producing work in m\n",
"N=1750#Speed of the pump in rpm\n",
"b1=0.025#Width of impeller at inlet per side in m\n",
"b2=0.023#Width of impeller at outlet in total in m\n",
"a11=90#The angle made by the entering fluid to impeller in degree\n",
"b22=27#Vanes set back angle at outlet in degree\n",
"Qloss=2.25#Leakage loss in l/s\n",
"ml=1.04#Mechanical loss in kW\n",
"cf=0.87#Contraction factor due to vane thickness \n",
"n0=0.55#Overall efficiency\n",
"d=1000#Density of water in kg/m**3\n",
"g=9.81#Acceleration due to gravity in m/s**2\n",
"\n",
"#calculations\n",
"U1=(3.1415*D1*N)/60#Blade inlet speed in m/s\n",
"A1=3.1415*D1*b1*cf*10**3#Area of flow at inlet in m**2\n",
"Qt=Q+Qloss#Total quantity of water handled by pump in l/s\n",
"Qts=Qt/2#Total quantity of water handled by pump per side in l/s\n",
"Cr1=(Qts*10**-3)/(A1*10**-3)#Flow velocity through impeller at inlet in m/s\n",
"b11=degrees(atan(Cr1/U1))#Inlet vane angle in degree\n",
"A2=3.1415*D2*(b2/2)*cf*10**3#Area of flow at outlet in m**2 here b2 is calculated per side\n",
"Cr2=Qts/A2#Velocity of flow at outlet in m/s\n",
"U2=(3.1415*D2*N)/60#Peripheral speed at outlet in m/s\n",
"Wx2=Cr2/tan(b22*pi/180)#Exit relative velocity in m/s\n",
"Cx2=U2-Wx2#Absolute whirl component at exit in m/s\n",
"a22=degrees(atan(Cr2/Cx2))#The absolute water angle at outlet in degree\n",
"C2=Cr2/sin(a22*pi/180)#Absolute velocity of water at exit in m/s\n",
"nh=Hm/((U2*Cx2)/g)#Manometric efficiency \n",
"nv=Q/Qt#Volumetric efficiency \n",
"SP=(d*g*(Q*10**-3/2)*Hm)/n0*10**-3#Shaft power in kW\n",
"nm=(SP-ml)/SP#Mechanical efficiency \n",
"\n",
"#output\n",
"print '(a)Inlet vane angle is %3.2f degree\\n(b)The absolute water angle is %3.2f degree\\n(c)Absolute velocity of water at exit is %3.2f m/s\\n(d)Manometric efficiency is %0.1f %%\\n(e)Volumetric efficiency is %0.2f %%\\n(f)Mechanical efficiency is %0.1f %%'%(b11,a22,C2,nh*100,nv*100,nm*100)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a)Inlet vane angle is 31.67 degree\n",
"(b)The absolute water angle is 13.07 degree\n",
"(c)Absolute velocity of water at exit is 18.74 m/s\n",
"(d)Manometric efficiency is 60.7 %\n",
"(e)Volumetric efficiency is 97.09 %\n",
"(f)Mechanical efficiency is 94.8 %\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 8.6 Page 360"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#input data\n",
"Hi=0.25#Vaccum gauge reading in m of Hg vaccum\n",
"P0=1.5#Pressure gauge reading in bar\n",
"Z01=0.5#Effective height between gauges in m\n",
"P=22#Power of electric motor in kW\n",
"Di=0.15#Inlet diameter in m\n",
"Do=0.15#Outlet diameter in m\n",
"Q=0.1#Discharge of pump in m**3/s\n",
"dHg=13600#Density of mercury in kg/m**3\n",
"dw=1000#Density of water in kg/m**3\n",
"g=9.81#Acceleration due to gravity in m/s**2\n",
"\n",
"#calculations\n",
"Pi=dHg*g*Hi#Inlet pressure in N/m**2 vaccum\n",
"Po=P0*10**5#Outlet pressure in N/m**2\n",
"V0=Q/((3.1415*Do**2)/4)#Velocity of water in delivery pipe in m/s\n",
"Vi=V0#vleocity of water in suction pipe in m/s\n",
"Hm=((Po+Pi)/(dw*g))+((V0**2-Vi**2)/(2*g))+(Z01)#Manometric head in m\n",
"n0=(dw*g*Q*Hm)/(P*10**3)#Overall efficiency \n",
"\n",
"#output\n",
"print '(a)Manometric head is %3.2f m\\n(b)Overall efficiency is %0.1f %%'%(Hm,n0*100)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a)Manometric head is 19.19 m\n",
"(b)Overall efficiency is 85.6 %\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 8.7 Page 361"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#input data\n",
"Hm=20#Head against which work is produced in pump in m\n",
"b22=45#Vanes set back angle at outlet in degree\n",
"N=600#Rotating speed of pump in rpm\n",
"Cr1=2#Flow velocity through impeller at inlet in m/s\n",
"Cr2=Cr1#Flow velocity through impeller at outlet in m/s\n",
"g=9.81#acceleration due to gravity in m/s**2\n",
"\n",
"#calculations\n",
"Wx2=Cr2/tan(b22*pi/180)#Exit relative velocity in m/s\n",
"U2=(4+(16+(4*3*792.8))**(1/2))/(2*3)# Blade outlet speed in m/s\n",
" #The above equation is obtained by solving \n",
" #Cx2=U2-Wx2 #Absolute whirl component at exit in m/s\n",
" #C2=(Cx2**2+Cr2**2)**(1/2) #Absolute velocity of water at exit in m/s\n",
" #Hm=(U2*Cx2/g)-((C2**2)/(4*g)) #Total head producing work in m\n",
" #3*(U2**2)-(4*U2)-792.8=0 \n",
"D2=(60*U2)/(3.1415*N)#Impeller diameter in m\n",
"\n",
"#output\n",
"print 'The impeller diameter is %3.4f m'%(D2)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The impeller diameter is 0.5391 m\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 8.8 Page 362"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#input data\n",
"n0=0.7#Overall efficiency\n",
"Q=0.025#Discharge of water by the pump in m**3/s\n",
"H=20#Height of supplied by the pump in m\n",
"D=0.1#Diameter of the pump in m\n",
"L=100#Length of the pipe in m\n",
"f=0.012#Friction coefficient \n",
"g=9.81#Acceleration due to gravity in m/s**2\n",
"d=1000#Density of water in kg/m**3\n",
"\n",
"#calculations\n",
"V0=Q/((3.1415/4)*D**2)#Velocity of water in the pipe in m/s\n",
"hf0=(4*f*L*V0**2)/(2*g*D)#Loss of head due to friction in pipe in m\n",
"Hm=H+hf0+(V0**2/(2*g))#Manometric head in m\n",
"P=(d*g*Q*Hm)/(n0)*10**-3#Power required to drive the pump in kW\n",
"\n",
"#output\n",
"print 'Power required to drive the pump is %3.2f kW'%(P)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Power required to drive the pump is 15.87 kW\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 8.9 Page 363"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#input data\n",
"Q=0.015#Discharge of water in pump in m**3/s\n",
"D1=0.2#Internal diameter of the impeller in m\n",
"D2=0.4#External diameter of the impeller in m\n",
"b1=0.016#Width of impeller at inlet in m\n",
"b2=0.008#Width of impeller at outlet in m\n",
"N=1200#Running speed of the pump in rpm\n",
"b22=30#Impeller vane angle at outlet in degree\n",
"g=9.81#Acceleration due to gravity in m/s**2\n",
"d=1000#Density of water in kg/m**3\n",
"\n",
"#calculations\n",
"print 'From velocity triangles the following values have been deduced'\n",
"a11=90#The absolute water angle at inlet in degree\n",
"Cx1=0#Absolute whirl component at inlet in m/s\n",
"A1=3.1415*D1*b1#Area of flow at inlet in m**2\n",
"Cr1=Q/A1#Flow velocity through impeller at inlet in m/s\n",
"C1=Cr1#Absolute velocity at inlet in m/s\n",
"A2=3.1415*D2*b2#Area of flow at outlet in m**2\n",
"Cr2=Q/A2#Flow velocity through impeller at outlet in m/s\n",
"U2=(3.1415*D2*N)/60#Blade outlet speed in m/s\n",
"Cx2=U2-(Cr2/tan(b22*pi/180))#Absolute whirl component at outlet in m/s\n",
"C2=(Cx2**2+Cr2**2)**(1/2)#Velocity at impeller exit in m/s\n",
"Ihl=((Cx2*U2)/g)-((C2**2)/(2*g))+((C1**2)/(2*g))#Pressure rise in impeller in m\n",
"\n",
"#output\n",
"print '\\n\\nThe rise in pressure in the impeller is %3.3f m'%(Ihl)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"From velocity triangles the following values have been deduced\n",
"\n",
"\n",
"The rise in pressure in the impeller is 31.852 m\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 8.10 Page 365"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#input data\n",
"Ihl=3#Head loss in impeller in m\n",
"Cr2=4.64#Flow velocity through impeller at outlet in m/s\n",
"U2=30#Blade outlet speed in m/s\n",
"dPi=35.3#Difference in pressure gauge readings at impeller inlet and outlet in m of water\n",
"Pg=4.7#Pressure gain in the casing in m of water \n",
"n=0.385#Part of absolute kinetic energy converted into pressure gain\n",
"g=9.81#Acceleration due to gravity in m/s**2\n",
"d=1000#Density of water in kg/m**3\n",
"ss=0.85#Slip coefficient\n",
"\n",
"#calculations\n",
"Kei=Pg/n#Kinetic energy at impeller exit in m/s\n",
"C2=((Kei)*2*g)**(1/2)#Velocity at impeller exit in m/s\n",
"Cx22=(C2**2-Cr2**2)**(1/2)#Absolute whirl component at outlet with fliud slip in m/s\n",
"Cx2=Cx22/ss#Ideal absolute whirl velocity in m/s\n",
"b22=degrees(atan(Cr2/(U2-Cx2)))#Blade angle at exit in degree\n",
"Wm=ss*U2*Cx2#Euler work input in J/kg\n",
"nm=dPi/(U2*Cx22/g)#Manometric efficiency\n",
"dP=(U2*Cx22/g)-(Ihl)-(C2**2/(2*g))#Pressure rise in impeller in m\n",
"\n",
"#output\n",
"print '(a)\\n Exit blade angle is %3.2f degree\\n Euler work input is %3.2f J/kg\\n(b)Manometric efficiency is %0.2f %%\\n(c)Pressure rise in the impeller is %3.3f m'%(b22,Wm,nm*100,dP)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a)\n",
" Exit blade angle is 20.17 degree\n",
" Euler work input is 442.93 J/kg\n",
"(b)Manometric efficiency is 78.18 %\n",
"(c)Pressure rise in the impeller is 29.943 m\n"
]
}
],
"prompt_number": 10
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 8.11 Page 366"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#input data\n",
"r1=0.051#Eye radius of the impeller in m\n",
"D2=0.406#Outer diameter of the impeller in m\n",
"b11=(90-75)#Inlet blade angle measured from tangential flow direction in degree\n",
"b22=(90-83)#Outlet blade angle measured from tangential flow direction in degree\n",
"b=0.064#Blade depth in m\n",
"Cx1=0#Inlet whirl velocity in m/s\n",
"nh=0.89#Hydraulic efficiency \n",
"g=9.81#Acceleration due to gravity in m/s**2\n",
"d=1000#Density of water in kg/m**3\n",
"N=900#Rotating speed of impeller in rpm\n",
"\n",
"#calculations\n",
"w=(2*3.1415*N)/60#Angular velocity at inlet in rad/s\n",
"U1=(w*r1)#Inlet tangential impeller velocity in m/s\n",
"C1=U1*tan(b11*pi/180)#Velocity at impeller inlet in m/s\n",
"A=2*3.1415*r1*b#Area of flow through the pump in m**2\n",
"Cr1=C1#Flow velocity through impeller at inlet in m/s\n",
"Q=A*Cr1#Volume flow through the pump in m**3/s\n",
"r2=D2/2#Outer radius of the impeller in m\n",
"Cr2=(r1*Cr1)/r2#Flow velocity through impeller at outlet in m/s\n",
"U2=w*r2#Outlet tangential impeller velocity in m/s\n",
"Wx2=Cr2/tan(b22*pi/180)#Exit relative velocity in m/s\n",
"E=(U2/g)*(U2-Wx2)#Theoretical head developed in m\n",
"Hm=nh*E#Total stagnation head developed by the pump in m\n",
"dP021=Hm*d*g*10**-3#Total pressure head coefficient in kPa\n",
"Cx2=U2-(Cr2/tan(b22*pi/180))#Absolute whirl velocity in m/s\n",
"C2=(Cr2**2+Cx2**2)**(1/2)#Velocity at impeller exit in m/s\n",
"dP21=(Hm-(((C2**2)-(C1**2))/(2*g)))*d*g*10**-3#The static pressure head in kPa\n",
"P=d*g*Q*Hm*10**-3#Power given to the fluid in kW\n",
"Ps=P/nh#Input power to impeller in kW\n",
"\n",
"#output\n",
"print '(a)Volume flow rate through the impeller is %3.4f m**3/s\\n(b)\\n stagnation pressure rise across the impeller is %3.1f kPa\\n Static pressure rise across the impeller is %3.1f kPa\\n(c)Power given to fluid is %3.2f kW\\n(d)Input power to impeller is %3.2f kW'%(Q,dP021,dP21,P,Ps)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a)Volume flow rate through the impeller is 0.0264 m**3/s\n",
"(b)\n",
" stagnation pressure rise across the impeller is 280.9 kPa\n",
" Static pressure rise across the impeller is 145.6 kPa\n",
"(c)Power given to fluid is 7.42 kW\n",
"(d)Input power to impeller is 8.34 kW\n"
]
}
],
"prompt_number": 11
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 8.12 Page 368"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from math import pi, tan\n",
"from __future__ import division\n",
"#input data\n",
"Q=0.04#Discharge of the pump design in m**3/s\n",
"Ns=0.075#Specific speed in rev\n",
"b22=(180-120)#Outlet angle with the normal in degree\n",
"H=35#Distance to which pumping of water is done in m\n",
"Dp=0.15#Diameter of suction and delivery pipes in m\n",
"L=40#Combined length of suction and delivery pipes in m\n",
"WD=1/10#Width to diameter ratio at outlet of impeller \n",
"f=0.005#Friction factor \n",
"g=9.81#Acceleration due to gravity in m/s**2\n",
"nh=0.76#Hydraulic effficiency neglecting the slip\n",
"n=0.06#Percentage occupied by blades on circumference area\n",
"\n",
"#calculations\n",
"A=(pi/4)*(Dp**2)#Area of flow in pipe in m**2\n",
"V=Q/A#Velocity in the pipes in m/s\n",
"OL=3*V**2/(2*g)#Other loses in the pipes in m\n",
"TL=(4*f*L*V**2/(2*g*Dp))+(OL)#Total loses in a pipe in m\n",
"TH=TL+H#Total required head in m\n",
"N=(Ns*((g*TH)**(3/4)))/((Q)**(1/2))#The speed of the pump in rev/s\n",
"from sympy import symbols, solve\n",
"from sympy import N as NN\n",
"D = symbols('D')\n",
"Ao=pi*WD*(1-n)*D**2#Flow area perpendicular to impeller outlet periphery \n",
"Cr2=Q/Ao#Flow velocity through impeller at outlet in m/s\n",
"U2=pi*D*N#Outlet tangential impeller velocity in m/s\n",
"Cx2=(g*TH)/(U2*nh)#Absolute whirl velocity in m/s\n",
"expr = tan(b22*pi/180)-(Cr2/(Cx2-U2)) # polynomial of D\n",
"D = solve(expr, D) # discarding -ve values \n",
"D = D[2] # Now discard imaginary part as negligible(in powers of e**-23)\n",
"D = NN(abs(D),3) # in meters # rounding off\n",
"#output\n",
"print 'The pump impeller diameter is %3.3f m'%(D)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The pump impeller diameter is 0.214 m\n"
]
}
],
"prompt_number": 12
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 8.13 Page 370"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#input data\n",
"N=2875#Speed of the pump in rpm \n",
"Q=57.2/3600#Discharge of the pump in m**3/s\n",
"Hm=42.1#Total head developed by the pump in m\n",
"d=1000#Density of the water in kg/m**3\n",
"g=9.81#Acceleration due to gravity in m/s**2\n",
"n=0.76#Efficiency of the pump\n",
"\n",
"#calculations\n",
"Ns=(N*Q**(1/2))/(Hm**(3/4))#Specific speed of the pump \n",
"P=((d*g*Q*Hm)/n)*10**-3#Power input in kW\n",
"\n",
"#calculations\n",
"print '(a)Specific speed of the pump is %3.f\\n(b)Power input is %3.3f kW'%(Ns,P)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a)Specific speed of the pump is 22\n",
"(b)Power input is 8.634 kW\n"
]
}
],
"prompt_number": 13
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 8.14 Page 371"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from math import ceil\n",
"#input data\n",
"D1=0.6#Inlet impeller diameter in m\n",
"D2=1.2#Outlet impeller diameter in m\n",
"Cr2=2.5#Radial flow velocity in m/s\n",
"N=200#Running speed of the pump in rpm\n",
"Q=1.88#Discharge of the pump in m**3/s\n",
"Hm=6#Head which the pump has to overcome in m\n",
"b22=26#Vane angle at exit at tangent to impeller in degree\n",
"d=1000#Density of the water in kg/m**3\n",
"g=9.81#Acceleration due to gravity in m/s**2\n",
"\n",
"#calculations\n",
"U2=(3.1415*D2*N)/60#Outlet tangential impeller velocity in m/s\n",
"Wx2=Cr2/tan(b22*pi/180)#Exit relative velocity in m/s\n",
"Cx2=U2-Wx2#Absolute whirl velocity in m/s\n",
"nm=(Hm/(U2*Cx2/g))#Manometric efficiency \n",
"Nls=((2*g*Hm*60**2)/((3.1415**2)*((1.2**2)-(0.6**2))))**(1/2)#Least starting speed of the pump in rpm\n",
"\n",
"#output\n",
"print '(1)Manometric efficiency is %0.1f %%\\n(2)Least speed to start the pump is %3.2f rpm, rounding off = %0.f rpm'%(nm*100,Nls, ceil(Nls))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(1)Manometric efficiency is 63.0 %\n",
"(2)Least speed to start the pump is 199.40 rpm, rounding off = 200 rpm\n"
]
}
],
"prompt_number": 14
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 8.15 Page 372"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#input data\n",
"D2=1.25#External diameter of the impeller in m\n",
"D1=0.5#Internal diameter of the impeller in m\n",
"Q=2#Discharge of the pump in m**3/s\n",
"Hm=16#Head over which pump has to operate in m\n",
"N=300#Running speed of the pump in rpm\n",
"b22=30#Angle at which vanes are curved back in degree\n",
"Cr1=2.5#Flow velocity through impeller at inlet in m/s\n",
"Cr2=Cr1#Flow velocity through impeller at outlet in m/s\n",
"d=1000#Density of the water in kg/m**3\n",
"g=9.81#Acceleration due to gravity in m/s**2\n",
"\n",
"#calculations\n",
"U2=(3.1415*D2*N)/60#Outlet tangential impeller velocity in m/s\n",
"Wx2=Cr2/tan(b22*pi/180)#Exit relative velocity in m/s\n",
"Cx2=U2-Wx2#Absolute whirl velocity in m/s\n",
"nm=(Hm*g)/(U2*Cx2)#Manometric or hydraulic efficiency\n",
"m=d*Q#Mass flow rate of water in kg/s\n",
"W=m*U2*Cx2*10**-3#Fluid power developed by the impeller in kW\n",
"Ps=W#Power required by the pump in kW neglecting mechanical loses\n",
"Nls=((2*g*Hm)/(((3.1415/60)**2)*(D2**2-D1**2)))**(1/2)#Minimum starting speed of the pump in rpm\n",
"\n",
"#output\n",
"print '(a)Manometric or hydraulic efficiency is %0.1f %% \\n(b)Power required by the pump is %3.2f kW\\n(c)Minimum starting speed of the pump is %3.1f rpm'%(nm*100,Ps,Nls)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a)Manometric or hydraulic efficiency is 52.2 % \n",
"(b)Power required by the pump is 600.98 kW\n",
"(c)Minimum starting speed of the pump is 295.4 rpm\n"
]
}
],
"prompt_number": 15
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 8.16 Page 373"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#input data\n",
"n=3#Number of stages \n",
"D2=0.4#Outlet impeller diameter in m\n",
"b2=0.02#Outlet impeller width in m\n",
"b22=45#Backward vanes angle at outlet in degree\n",
"dA=0.1#Reduction in circumferential area\n",
"nm=0.9#Manometric efficiency of the pump\n",
"Q=0.05#Discharge of the pump in m**3/s\n",
"N=1000#Running speed of the pump in rpm\n",
"n0=0.8#Overall efficiency of the pump\n",
"g=9.81#Acceleration due to gravity in m/s**2\n",
"d=1000#Density of water in kg/m**3\n",
"\n",
"#calculations\n",
"A2=(1-dA)*3.1415*D2*b2#Area of flow at outlet in m**2\n",
"Cr2=Q/A2#Flow velocity through impeller at outlet in m/s\n",
"U2=(3.1415*D2*N)/60#Outlet impeller tangential velocity in m/s\n",
"Wx2=Cr2#Exit relative velocity in m/s as tand(b22)=1\n",
"Cx2=U2-Wx2#Absolute whirl velocity in m/s\n",
"Hm=(nm*U2*Cx2)/g#Head over which pump has to operate in m\n",
"H=n*Hm#Total head generated by the pump in m\n",
"P=d*g*Q*Hm*n#Power output from the pump in W\n",
"Ps=P/n0*10**-3#Shaft power input in kW\n",
"\n",
"#output\n",
"print '(1)The head generated by the pump is %3.2f m\\n(2)Shaft power input is %3.3f kW'%(H,Ps)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(1)The head generated by the pump is 107.98 m\n",
"(2)Shaft power input is 66.205 kW\n"
]
}
],
"prompt_number": 16
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 8.17 Page 374"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#input data\n",
"H=156#Total head operated by the pumps in m\n",
"N=1000#Running speed of the pump in rpm\n",
"Ns=20#Specific speed of each pump \n",
"Q=0.150#Discharge of the pump in m**3/s\n",
"\n",
"#calculations\n",
"Hm=((N*(Q)**(1/2))/(Ns))**(4/3)#Head developed by each pump in m\n",
"n=H/Hm#Number of pumps\n",
"\n",
"#output\n",
"print 'The number of pumps are %3.f'%(n)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The number of pumps are 3\n"
]
}
],
"prompt_number": 17
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 8.18 Page 375"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#input data\n",
"Q1=120#Discharge of each of the multi stage pump in parallel in first case in m**3/s\n",
"Q2=450#Discharge of the multi stage pump in second case in m**3/s\n",
"H1=16#Head of each stage in first case in m\n",
"D1=0.15#Diameter of impeller in first case in m\n",
"H=140#Total head developed by all pumps in second case in m\n",
"N1=1500#Running speed of the pump in rpm in first case\n",
"N2=1200#Running speed of the pump in rpm in second case\n",
"#calculations\n",
"H2=H1*((Q2/Q1)*((N2/N1)**2))**(4/6)#Head of each stage in second case in m\n",
"n=H/H2#Number of stages in second case \n",
"D2=D1*(((N1/N2)**(2))*(H2/H1))**(1/2)#Diameter of impeller in second case in m\n",
"\n",
"#output\n",
"print '(a)number of stages required is %3.f\\n(b)Diameter of impeller in the second case is %3.2f m or %0.f mm'%(n,D2, D2*1000)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a)number of stages required is 5\n",
"(b)Diameter of impeller in the second case is 0.25 m or 251 mm\n"
]
}
],
"prompt_number": 18
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 8.19 Page 376"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#input data\n",
"H=36#Initial total head of the pump in m\n",
"Q1=0.05#Initial discharge of the pump in m**3/s\n",
"H2=3.5#Sum of static pressure and velocity head at inlet in m\n",
"P01=0.75#Atmospheric pressure initially in m of Hg\n",
"Pvap1=1.8*10**3#Vapour pressure of water initially in Pa\n",
"Pvap2=830#Vapour pressure of water finanlly in Pa\n",
"P02=0.62#Atmospheric pressure finally in m of Hg\n",
"g=9.81#Acceleration due to gravity in m/s**2\n",
"dW=1000#Density of water in kg/m**3\n",
"dHg=13.6#Density of mercury in kg/m**3\n",
"\n",
"#calculations\n",
"NPSH=H2-((Pvap1)/(dW*g))#Net positive suction head in m\n",
"s=NPSH/H#Cavitation parameter when pump dvelops same total head and discharge \n",
"dH1=(P01*dHg)-(s*H)-(Pvap1/(dW*g))#The height reduced in initial condition above supply in m\n",
"dH2=(P02*dHg)-(s*H)-(Pvap2/(dW*g))#The height reduced in final condition above supply in m\n",
"Z=dH1-dH2#The total height which the pump must be lowered at new location in m\n",
"\n",
"#output\n",
"print '(a)The cavitation parameter is %3.4f\\n(b)\\n The height reduced in initial condition above supply is %3.1f m\\n The height reduced in final condition above supply is %3.2f m\\n The total height which the pump must be lowered at new location is %3.2f m'%(s,dH1,dH2,Z)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a)The cavitation parameter is 0.0921\n",
"(b)\n",
" The height reduced in initial condition above supply is 6.7 m\n",
" The height reduced in final condition above supply is 5.03 m\n",
" The total height which the pump must be lowered at new location is 1.67 m\n"
]
}
],
"prompt_number": 19
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 8.20 Page 377"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from math import degrees, atan\n",
"#input data\n",
"Dt=1#Impeller outlet diameter in m\n",
"Dh=0.5#Diameter of the boss in m\n",
"Ns=38#Specific speed of the pump \n",
"Ca=2#Velocity of the flow in m/s\n",
"H=6#Head which the pump has to drive in m\n",
"\n",
"#calculations\n",
"A=(3.1415/4)*(Dt**2-Dh**2)#Area of flow in m**2\n",
"Q=A*Ca#Discharge of the pump in m**3/s\n",
"N=(Ns*H**(3/4))/(Q**(1/2))#Pump speed in rpm\n",
"U1=(3.1415*Dh*N)/60#Blade inlet speed in m/s\n",
"b1=degrees(atan(Ca/U1))#Vane angle at the entry of the pump when the flow is axial at inlet in degree\n",
"\n",
"#output\n",
"print '(a)Pump speed is %0.2f rpm\\n(b)Vane angle at the entry of the pump when the flow is axial at inlet is %3.2f degree'%(N,b1)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a)Pump speed is 134.22 rpm\n",
"(b)Vane angle at the entry of the pump when the flow is axial at inlet is 29.65 degree\n"
]
}
],
"prompt_number": 20
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 8.21 Page 378"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#input data\n",
"Q=0.180#Discharge of the pump in m**3/s\n",
"H=2#Head developed by the pump in m\n",
"Ns=250#Specific speed of the pump \n",
"SR=2.4#Speed ratio of the pump\n",
"FR=0.5#Flow ratio of the pump\n",
"g=9.81#Acceleration due to gravity in m/s**2\n",
"\n",
"#calculations\n",
"N=(Ns*(H**(3/4)))/(Q**(1/2))#Pump speed in rpm\n",
"U=SR*(2*g*H)**(1/2)#Peripheral velocity in m/s\n",
"D=(60*U)/(3.1415*N)#Runner diameter of the pump in m\n",
"Ca=FR*(2*g*H)**(1/2)#Velocity of flow in m/s\n",
"Dh=((D**2)-(Q*4/(Ca*3.14)))**(1/2)#Boss diameter of the pump in m\n",
"\n",
"#output\n",
"print '(a)Pump speed is %3.i rpm\\n(b)Runner diameter of the pump is %3.2f m\\n(c)Boss diameter of the pump is %3.2f m\\n'%(N,D,Dh)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a)Pump speed is 991 rpm\n",
"(b)Runner diameter of the pump is 0.29 m\n",
"(c)Boss diameter of the pump is 0.10 m\n",
"\n"
]
}
],
"prompt_number": 21
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 8.22 Page 379"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#input data\n",
"Hs=2.5#Height of the pipe above suction reservoir in m\n",
"H1=18#Height of the pipe below supply reservoir in m\n",
"H=2.7#Total height through which the pump lifts water in m\n",
"Q1=2.75#Discharge of water used from supply reservoir in l/s\n",
"Qt=7.51#Discharge of water totally delivered in l/s\n",
"\n",
"#calculations\n",
"Hd=H-Hs#Height of the pipe from discharge reservoir in m\n",
"Qs=Qt-Q1#Discharge of water in delivery reservoir in l/s\n",
"nj=(Qs/Q1)*((Hs+Hd)/(H1-Hd))#Jet pump efficiency \n",
"\n",
"#output\n",
"print 'The efficiency of the jet pump is %0.1f'%(nj*100)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The efficiency of the jet pump is 26.3\n"
]
}
],
"prompt_number": 22
}
],
"metadata": {}
}
]
}